/*
 * A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
 *
 * Based on example code by Stefan Gustavson (stegu@itn.liu.se).
 * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
 * Better rank ordering method by Stefan Gustavson in 2012.
 *
 * This could be speeded up even further, but it's useful as it is.
 *
 * Version 2012-03-09
 *
 * This code was placed in the public domain by its original author,
 * Stefan Gustavson. You may use it as you see fit, but
 * attribution is appreciated.
 *
 */
package wblut.math;



public class WB_SNoise implements WB_Noise { // Simplex noise in 2D, 3D and 4D
	private static Grad grad3[] = { new Grad(1, 1, 0), new Grad(-1, 1, 0), new Grad(1, -1, 0), new Grad(-1, -1, 0),
			new Grad(1, 0, 1), new Grad(-1, 0, 1), new Grad(1, 0, -1), new Grad(-1, 0, -1), new Grad(0, 1, 1),
			new Grad(0, -1, 1), new Grad(0, 1, -1), new Grad(0, -1, -1) };

	private static Grad grad4[] = { new Grad(0, 1, 1, 1), new Grad(0, 1, 1, -1), new Grad(0, 1, -1, 1),
			new Grad(0, 1, -1, -1), new Grad(0, -1, 1, 1), new Grad(0, -1, 1, -1), new Grad(0, -1, -1, 1),
			new Grad(0, -1, -1, -1), new Grad(1, 0, 1, 1), new Grad(1, 0, 1, -1), new Grad(1, 0, -1, 1),
			new Grad(1, 0, -1, -1), new Grad(-1, 0, 1, 1), new Grad(-1, 0, 1, -1), new Grad(-1, 0, -1, 1),
			new Grad(-1, 0, -1, -1), new Grad(1, 1, 0, 1), new Grad(1, 1, 0, -1), new Grad(1, -1, 0, 1),
			new Grad(1, -1, 0, -1), new Grad(-1, 1, 0, 1), new Grad(-1, 1, 0, -1), new Grad(-1, -1, 0, 1),
			new Grad(-1, -1, 0, -1), new Grad(1, 1, 1, 0), new Grad(1, 1, -1, 0), new Grad(1, -1, 1, 0),
			new Grad(1, -1, -1, 0), new Grad(-1, 1, 1, 0), new Grad(-1, 1, -1, 0), new Grad(-1, -1, 1, 0),
			new Grad(-1, -1, -1, 0) };

	private short p[] = new short[256];
	// To remove the need for index wrapping, double the permutation table
	// length
	private short perm[] = new short[512];
	private short permMod12[] = new short[512];
	private double sx, sy, sz, sw;

	/**
	 *
	 */
	public WB_SNoise() {
		this(System.currentTimeMillis());
		sx = sy = sz = sw = 1.0;
	}

	/**
	 *
	 *
	 * @param seed
	 */
	public WB_SNoise(final long seed) {
		setSeed(seed);
		sx = sy = sz = sw = 1.0;
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#setSeed(long)
	 */
	@Override
	public void setSeed(long seed) {
		for (short i = 0; i < 256; i++) {
			p[i] = i;
		}
		seed = (seed * 6364136223846793005l) + 1442695040888963407l;
		seed = (seed * 6364136223846793005l) + 1442695040888963407l;
		seed = (seed * 6364136223846793005l) + 1442695040888963407l;
		for (int i = 255; i >= 0; i--) {
			seed = (seed * 6364136223846793005l) + 1442695040888963407l;
			int r = (int) ((seed + 31) % (i + 1));
			if (r < 0) {
				r += (i + 1);
			}
			p[r] = p[i];
		}
		for (int i = 0; i < 512; i++) {
			perm[i] = p[i & 255];
			permMod12[i] = (short) (perm[i] % 12);
		}
	}

	// Skewing and unskewing factors for 2, 3, and 4 dimensions
	private static final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
	private static final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
	private static final double F3 = 1.0 / 3.0;
	private static final double G3 = 1.0 / 6.0;
	private static final double F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
	private static final double G4 = (5.0 - Math.sqrt(5.0)) / 20.0;

	/**
	 *
	 *
	 * @param x
	 * @return
	 */
	// This method is a *lot* faster than using (int)Math.floor(x)
	private static int fastfloor(final double x) {
		int xi = (int) x;
		return x < xi ? xi - 1 : xi;
	}

	/**
	 *
	 *
	 * @param g
	 * @param x
	 * @param y
	 * @return
	 */
	private static double dot(final Grad g, final double x, final double y) {
		return (g.x * x) + (g.y * y);
	}

	/**
	 *
	 *
	 * @param g
	 * @param x
	 * @param y
	 * @param z
	 * @return
	 */
	private static double dot(final Grad g, final double x, final double y, final double z) {
		return (g.x * x) + (g.y * y) + (g.z * z);
	}

	/**
	 *
	 *
	 * @param g
	 * @param x
	 * @param y
	 * @param z
	 * @param w
	 * @return
	 */
	private static double dot(final Grad g, final double x, final double y, final double z, final double w) {
		return (g.x * x) + (g.y * y) + (g.z * z) + (g.w * w);
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#value1D(double)
	 */
	@Override
	public double value1D(final double x) {
		return value2D(x, 0);

	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#value2D(double, double)
	 */
	// 2D simplex noise
	@Override
	public double value2D(final double x, final double y) {
		double xin = sx * x;
		double yin = sy * y;
		double n0, n1, n2; // Noise contributions from the three corners
		// Skew the input space to determine which simplex cell we're in
		double s = (xin + yin) * F2; // Hairy factor for 2D
		int i = fastfloor(xin + s);
		int j = fastfloor(yin + s);
		double t = (i + j) * G2;
		double X0 = i - t; // Unskew the cell origin back to (x,y) space
		double Y0 = j - t;
		double x0 = xin - X0; // The x,y distances from the cell origin
		double y0 = yin - Y0;
		// For the 2D case, the simplex shape is an equilateral triangle.
		// Determine which simplex we are in.
		int i1, j1; // Offsets for second (middle) corner of simplex in (i,j)
		// coords
		if (x0 > y0) {
			i1 = 1;
			j1 = 0;
		} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
		else {
			i1 = 0;
			j1 = 1;
		} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
		// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
		// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
		// c = (3-sqrt(3))/6
		double x1 = (x0 - i1) + G2; // Offsets for middle corner in (x,y) unskewed
		// coords
		double y1 = (y0 - j1) + G2;
		double x2 = (x0 - 1.0) + (2.0 * G2); // Offsets for last corner in (x,y)
		// unskewed coords
		double y2 = (y0 - 1.0) + (2.0 * G2);
		// Work out the hashed gradient indices of the three simplex corners
		int ii = i & 255;
		int jj = j & 255;
		int gi0 = permMod12[ii + perm[jj]];
		int gi1 = permMod12[ii + i1 + perm[jj + j1]];
		int gi2 = permMod12[ii + 1 + perm[jj + 1]];
		// Calculate the contribution from the three corners
		double t0 = 0.5 - (x0 * x0) - (y0 * y0);
		if (t0 < 0) {
			n0 = 0.0;
		} else {
			t0 *= t0;
			n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for
			// 2D gradient
		}
		double t1 = 0.5 - (x1 * x1) - (y1 * y1);
		if (t1 < 0) {
			n1 = 0.0;
		} else {
			t1 *= t1;
			n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
		}
		double t2 = 0.5 - (x2 * x2) - (y2 * y2);
		if (t2 < 0) {
			n2 = 0.0;
		} else {
			t2 *= t2;
			n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
		}
		// Add contributions from each corner to get the final noise value.
		// The result is scaled to return values in the interval [-1,1].
		return 70.0 * (n0 + n1 + n2);
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#value3D(double, double, double)
	 */
	@Override
	public double value3D(final double x, final double y, final double z) {
		double xin = sx * x;
		double yin = sy * y;
		double zin = sz * z;
		double n0, n1, n2, n3; // Noise contributions from the four corners
		// Skew the input space to determine which simplex cell we're in
		double s = (xin + yin + zin) * F3; // Very nice and simple skew factor
		// for 3D
		int i = fastfloor(xin + s);
		int j = fastfloor(yin + s);
		int k = fastfloor(zin + s);
		double t = (i + j + k) * G3;
		double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
		double Y0 = j - t;
		double Z0 = k - t;
		double x0 = xin - X0; // The x,y,z distances from the cell origin
		double y0 = yin - Y0;
		double z0 = zin - Z0;
		// For the 3D case, the simplex shape is a slightly irregular
		// tetrahedron.
		// Determine which simplex we are in.
		int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k)
		// coords
		int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
		if (x0 >= y0) {
			if (y0 >= z0) {
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			} // X Y Z order
			else if (x0 >= z0) {
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			} // X Z Y order
			else {
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			} // Z X Y order
		} else { // x0<y0
			if (y0 < z0) {
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} // Z Y X order
			else if (x0 < z0) {
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} // Y Z X order
			else {
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			} // Y X Z order
		}
		// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
		// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z),
		// and
		// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z),
		// where
		// c = 1/6.
		double x1 = (x0 - i1) + G3; // Offsets for second corner in (x,y,z) coords
		double y1 = (y0 - j1) + G3;
		double z1 = (z0 - k1) + G3;
		double x2 = (x0 - i2) + (2.0 * G3); // Offsets for third corner in (x,y,z)
		// coords
		double y2 = (y0 - j2) + (2.0 * G3);
		double z2 = (z0 - k2) + (2.0 * G3);
		double x3 = (x0 - 1.0) + (3.0 * G3); // Offsets for last corner in (x,y,z)
		// coords
		double y3 = (y0 - 1.0) + (3.0 * G3);
		double z3 = (z0 - 1.0) + (3.0 * G3);
		// Work out the hashed gradient indices of the four simplex corners
		int ii = i & 255;
		int jj = j & 255;
		int kk = k & 255;
		int gi0 = permMod12[ii + perm[jj + perm[kk]]];
		int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
		int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
		int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];
		// Calculate the contribution from the four corners
		double t0 = 0.6 - (x0 * x0) - (y0 * y0) - (z0 * z0);
		if (t0 < 0) {
			n0 = 0.0;
		} else {
			t0 *= t0;
			n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
		}
		double t1 = 0.6 - (x1 * x1) - (y1 * y1) - (z1 * z1);
		if (t1 < 0) {
			n1 = 0.0;
		} else {
			t1 *= t1;
			n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
		}
		double t2 = 0.6 - (x2 * x2) - (y2 * y2) - (z2 * z2);
		if (t2 < 0) {
			n2 = 0.0;
		} else {
			t2 *= t2;
			n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
		}
		double t3 = 0.6 - (x3 * x3) - (y3 * y3) - (z3 * z3);
		if (t3 < 0) {
			n3 = 0.0;
		} else {
			t3 *= t3;
			n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
		}
		// Add contributions from each corner to get the final noise value.
		// The result is scaled to stay just inside [-1,1]
		return 32.0 * (n0 + n1 + n2 + n3);
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#value4D(double, double, double, double)
	 */
	// 4D simplex noise, better simplex rank ordering method 2012-03-09
	@Override
	public double value4D(final double x, final double y, final double z, final double w) {
		double xin = sx * x;
		double yin = sy * y;
		double zin = sz * z;
		double win = sw * w;
		double n0, n1, n2, n3, n4; // Noise contributions from the five corners
		// Skew the (x,y,z,w) space to determine which cell of 24 simplices
		// we're in
		double s = (xin + yin + zin + win) * F4; // Factor for 4D skewing
		int i = fastfloor(xin + s);
		int j = fastfloor(yin + s);
		int k = fastfloor(zin + s);
		int l = fastfloor(win + s);
		double t = (i + j + k + l) * G4; // Factor for 4D unskewing
		double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
		double Y0 = j - t;
		double Z0 = k - t;
		double W0 = l - t;
		double x0 = x - X0; // The x,y,z,w distances from the cell origin
		double y0 = y - Y0;
		double z0 = z - Z0;
		double w0 = w - W0;
		// For the 4D case, the simplex is a 4D shape I won't even try to
		// describe.
		// To find out which of the 24 possible simplices we're in, we need to
		// determine the magnitude ordering of x0, y0, z0 and w0.
		// Six pair-wise comparisons are performed between each possible pair
		// of the four coordinates, and the results are used to rank the
		// numbers.
		int rankx = 0;
		int ranky = 0;
		int rankz = 0;
		int rankw = 0;
		if (x0 > y0) {
			rankx++;
		} else {
			ranky++;
		}
		if (x0 > z0) {
			rankx++;
		} else {
			rankz++;
		}
		if (x0 > w0) {
			rankx++;
		} else {
			rankw++;
		}
		if (y0 > z0) {
			ranky++;
		} else {
			rankz++;
		}
		if (y0 > w0) {
			ranky++;
		} else {
			rankw++;
		}
		if (z0 > w0) {
			rankz++;
		} else {
			rankw++;
		}
		int i1, j1, k1, l1; // The integer offsets for the second simplex corner
		int i2, j2, k2, l2; // The integer offsets for the third simplex corner
		int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
		// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some
		// order.
		// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w
		// and x<w
		// impossible. Only the 24 indices which have non-zero entries make any
		// sense.
		// We use a thresholding to set the coordinates in turn from the largest
		// magnitude.
		// Rank 3 denotes the largest coordinate.
		i1 = rankx >= 3 ? 1 : 0;
		j1 = ranky >= 3 ? 1 : 0;
		k1 = rankz >= 3 ? 1 : 0;
		l1 = rankw >= 3 ? 1 : 0;
		// Rank 2 denotes the second largest coordinate.
		i2 = rankx >= 2 ? 1 : 0;
		j2 = ranky >= 2 ? 1 : 0;
		k2 = rankz >= 2 ? 1 : 0;
		l2 = rankw >= 2 ? 1 : 0;
		// Rank 1 denotes the second smallest coordinate.
		i3 = rankx >= 1 ? 1 : 0;
		j3 = ranky >= 1 ? 1 : 0;
		k3 = rankz >= 1 ? 1 : 0;
		l3 = rankw >= 1 ? 1 : 0;
		// The fifth corner has all coordinate offsets = 1, so no need to
		// compute that.
		double x1 = (x0 - i1) + G4; // Offsets for second corner in (x,y,z,w)
		// coords
		double y1 = (y0 - j1) + G4;
		double z1 = (z0 - k1) + G4;
		double w1 = (w0 - l1) + G4;
		double x2 = (x0 - i2) + (2.0 * G4); // Offsets for third corner in (x,y,z,w)
		// coords
		double y2 = (y0 - j2) + (2.0 * G4);
		double z2 = (z0 - k2) + (2.0 * G4);
		double w2 = (w0 - l2) + (2.0 * G4);
		double x3 = (x0 - i3) + (3.0 * G4); // Offsets for fourth corner in
		// (x,y,z,w) coords
		double y3 = (y0 - j3) + (3.0 * G4);
		double z3 = (z0 - k3) + (3.0 * G4);
		double w3 = (w0 - l3) + (3.0 * G4);
		double x4 = (x0 - 1.0) + (4.0 * G4); // Offsets for last corner in (x,y,z,w)
		// coords
		double y4 = (y0 - 1.0) + (4.0 * G4);
		double z4 = (z0 - 1.0) + (4.0 * G4);
		double w4 = (w0 - 1.0) + (4.0 * G4);
		// Work out the hashed gradient indices of the five simplex corners
		int ii = i & 255;
		int jj = j & 255;
		int kk = k & 255;
		int ll = l & 255;
		int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
		int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
		int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
		int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
		int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
		// Calculate the contribution from the five corners
		double t0 = 0.6 - (x0 * x0) - (y0 * y0) - (z0 * z0) - (w0 * w0);
		if (t0 < 0) {
			n0 = 0.0;
		} else {
			t0 *= t0;
			n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
		}
		double t1 = 0.6 - (x1 * x1) - (y1 * y1) - (z1 * z1) - (w1 * w1);
		if (t1 < 0) {
			n1 = 0.0;
		} else {
			t1 *= t1;
			n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
		}
		double t2 = 0.6 - (x2 * x2) - (y2 * y2) - (z2 * z2) - (w2 * w2);
		if (t2 < 0) {
			n2 = 0.0;
		} else {
			t2 *= t2;
			n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
		}
		double t3 = 0.6 - (x3 * x3) - (y3 * y3) - (z3 * z3) - (w3 * w3);
		if (t3 < 0) {
			n3 = 0.0;
		} else {
			t3 *= t3;
			n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
		}
		double t4 = 0.6 - (x4 * x4) - (y4 * y4) - (z4 * z4) - (w4 * w4);
		if (t4 < 0) {
			n4 = 0.0;
		} else {
			t4 *= t4;
			n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
		}
		// Sum up and scale the result to cover the range [-1,1]
		return 27.0 * (n0 + n1 + n2 + n3 + n4);
	}

	// Inner class to speed upp gradient computations
	// (array access is a lot slower than member access)
	private static class Grad {
		double x, y, z, w;

		/**
		 *
		 *
		 * @param x
		 * @param y
		 * @param z
		 */
		Grad(final double x, final double y, final double z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		/**
		 *
		 *
		 * @param x
		 * @param y
		 * @param z
		 * @param w
		 */
		Grad(final double x, final double y, final double z, final double w) {
			this.x = x;
			this.y = y;
			this.z = z;
			this.w = w;
		}
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#setScale(double)
	 */
	@Override
	public void setScale(final double sx) {
		this.sx = sx;
		this.sy = sx;
		this.sz = sx;
		this.sw = sx;
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#setScale(double, double)
	 */
	@Override
	public void setScale(final double sx, final double sy) {
		this.sx = sx;
		this.sy = sy;
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#setScale(double, double, double)
	 */
	@Override
	public void setScale(final double sx, final double sy, final double sz) {
		this.sx = sx;
		this.sy = sy;
		this.sz = sz;
	}

	/* (non-Javadoc)
	 * @see wblut.math.WB_Noise#setScale(double, double, double, double)
	 */
	@Override
	public void setScale(final double sx, final double sy, final double sz, final double sw) {
		this.sx = sx;
		this.sy = sy;
		this.sz = sz;
		this.sw = sw;
	}

}